Due Apr 20, 2:59 AM EDT
Choose the correct statement about the derivative:
Correct!
Find the derivative of (sinx)cosx (pay attention to the fact that this function is different from both exponential and polynomial ones).
Find the equation of tangent line of the function f(x)=ex/x at the point x=1. Write in the form Kx+B.
Find the approximate value of the expression (1.99)7 by using linear approximation.
Choose correct statements about extrema and convexity:
Correct!
Correct!
For the function x2(1−x2) find the value f′′(0) and define whether it convex, concave or neither. Write found value and the answer to the question ("CONVEX", "CONCAVE" or "NONE"), separated by semicolon.
Consider the function f(x)=x⋅e−x. Find its local extremum (there is only one); write its coordinate and the type ("MAXIMUM" or "MINIMUM"), separate with semi-colon.